Known in the art is an internal combustion engine wherein an NOx storing and reducing catalyst storing NOx contained in exhaust gas when an air-fuel ratio of inflowing exhaust gas is lean and releasing the stored NOx when the air-fuel ratio of the inflowing exhaust gas becomes the stoichiometric air-fuel ratio or rich is arranged in an engine exhaust passage (see for example Japanese-Patent Publication (A) No. 2003-129829). In this internal combustion engine, when combustion is performed under a lean air-fuel ratio, the generated NOx is stored in the NOx storing and reducing catalyst. On the other hand, when the NOx storage ability of the NOx storing and reducing catalyst approaches saturation, the air-fuel ratio of the exhaust gas is temporarily made rich whereby NOx is released from the NOx storing and reducing catalyst and reduced.
However, if the amount of NOx discharged from the combustion chambers increases, the amount of consumption of post-treatment use fuel fed for making the air-fuel ratio of the exhaust gas rich for releasing the NOx from the NOx storing and reducing catalyst increases and, as the degree of deterioration of the NOx storing and reducing catalyst increases, the amount of consumption of this post-treatment use fuel increases. On the other hand, if for example the fuel injection timing, one operating parameter of the engine, is advanced, the combustion temperature rises, so the amount of generation of NOx increases, but the combustion efficiency rises, so the fuel injection amount, that is, the amount of combustion of the combustion use fuel, is decreased.
If an operating state is made a state where the amount of NOx generated in the combustion chambers increases in this way, the amount of consumption of the combustion use fuel decreases, but the amount of consumption of post-treatment use fuel increases. Conversely to this, if the operating state is made a state where the amount of NOx generated in the combustion chambers decreases, the amount of consumption of the combustion use fuel increases, but the amount of consumption of the post-treatment use fuel decreases. In this case, maintaining the amount of NOx discharged into the atmosphere at below the regulatory value is an absolute condition. What is demanded the most under such a condition is that the total amount of consumption of combustion use fuel and post-treatment use fuel per set driving distance of the fuel be reduced as much as possible. That is, it is demanded that the engine be set in an operating state where the total amount of consumption of fuel per set driving distance becomes the smallest, in other words, an operating state where the amount of CO2 discharged per set driving distance becomes the smallest.
In this case, as explained above, the higher the degree of deterioration of the NOx storing and reducing catalyst, the greater the amount of consumption of post-treatment use fuel, so the operating state where the total amount of consumption of the fuel becomes smallest changes depending on the degree of deterioration of the NOx storing and reducing catalyst. In this way, when purifying the exhaust gas of the harmful components, it is necessary to consider the total amount of consumption of the fuel including not only the amount of consumption of the post-treatment use fuel, but also the amount of consumption of the combustion use fuel. In the past, the total amount of consumption of the fuel was not considered at all. Therefore, in the past, there was the problem that the amount of consumption of fuel per set driving distance, that is, the amount of CO2 exhausted per set driving distance, could not be minimized.